HELP ASAP 80 POINTS (AND N LINKS OR DOWNLOADS) Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.

4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.

5. Explain what the solution means in the context of the word problem.

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.